Gainesville Cigar stocks Cuban cigars that have variable lead times because of t

Question

Gainesville Cigar stocks Cuban cigars that have variable lead times because of the difficulty in importing the product: lead time is normally distributed with an average of 5 weeks and a standard deviation of 1 week. Demand is a variable with normal distribution with mean of 100 cigars per week with a standard deviation of 10 cigars. a.) For a 90% service level, what is the ROP? b.) What is the ROP for a 95% service level? c.) Explain what these two service levels mean. Which is preferable? Gainesville Cigar stocks Cuban cigars that have variable lead times because of the difficulty in importing the product: lead time is normally distributed with an average of 5 weeks and a standard deviation of 1 week. Demand is a variable with normal distribution with mean of 100 cigars per week with a standard deviation of 10 cigars. a.) For a 90% service level, what is the ROP? b.) What is the ROP for a 95% service level? c.) Explain what these two service levels mean. Which is preferable? a.) For a 90% service level, what is the ROP? b.) What is the ROP for a 95% service level? c.) Explain what these two service levels mean. Which is preferable?

Explanation / Answer

A.

At a service level of 90%,

Value of Z = 1.29

Reorder point = D*LT + Z*(LT*SDd^2 + D^2*SDlt^2)^.5

Here,

D = average weekly demand

LT = average lead time

SDd = Standard deviation of demand

SDlt = Standard deviation of lead time

So,

Reorder point = 100*5 + 1.29*(5*10^2 + 100^2 * 1^2)^.5

Reorder point = 632.19 or 632 units

B.

If service level is 95%,

Then the value of Z = 1.65

Reorder point = D*LT + Z*(LT*SDd^2 + D^2*SDlt^2)^.5

Reorder point = 100*5 + 1.65*(5*10^2 + 100^2 * 1^2)^.5

Reorder point = 669 .07 or 669 units

C.

A higher service level means, a lower risk of stock out in the operation. It means that if an organization wants to reduce the probability of stock out and its cost, then the organization must chose the relatively higher level of service or Z value. In the given case, the 95% service level comes at 669 units of ROP in comparison to the 632 units at 90% service level. Hence the risk of stock out comes down at 95% service level.

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